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Anime (Animated)

Dead Leaves
Two people wake up in an open field with no memory of how they got there. One has a tv for a head, the other is a sexy woman with a black patch around her eye. They immediately go on a crime spree and end up in maximum security prison on what's left of the moon. Insanity ensues.
Koukaku Kidoutai (1995)
The year is 2029. Much of the world has cybernetic implants. Japan's Section 9 (a cybercrimes division), takes on whom they assume is a hacker named The Puppet Master, who is hacking the 'ghosts' of ordinary citizens as well as political leaders in an attempt to control them. What they discover instead has heavy ramifications for the entire world, and especially Major Kusanagi of Section 9. Heavy cyberpunk, police, and girls & guns action by famed mangaka Shirow Masamune.
Neko No Ongaeshi
Miyazaki/Studio Ghibli sequel.
Parasite Dolls (movie version) (2004)
The year is 2034, and AI androids called Boomers are commonplace in the city of MegaTokyo. A movie version of a side story to the OVA series, AD Police (which itself is a side story to the BubbleGum Crisis series), which focuses on a secret branch of the AD Police. Expands upon the series universe as a whole, giving it a much more fleshed out feel in a Blade Runner-esque world. Several short stories combined into one. Helmed by famous names in anime. Cyberpunk themes.
Tenku No Shiro Raputa (1986)
Sheeta and Pazu journey together to the flying island of Laputa to unlock its secrets--and the secrets of Sheeta's own heritage.